With the development of large-bandwidth and high-speed electronic analog-to-digital converters (ADCs) and photo detectors (PDs), coherent detection with digital signal processing (DSP) has been attracting a great deal of interest in research community. It is well known that coherent detection can include either homodyne detection or heterodyne detection. However, unlike homodyne detection, heterodyne detection can simultaneously down-convert in-phase (I) and quadrature (Q) components to an intermediate frequency (IF), thereby reducing the number of balanced PDs and ADCs of a coherent receiver by half. Furthermore, with heterodyne detection there is no need to consider the delays between the I and Q components in a polarization-division-multiplexed (PDM) signal. In addition, with heterodyne detection a conventional dual-hybrid structure is also unnecessary. Accordingly, heterodyne detection is much more hardware-efficient than homodyne detection.
However, the ADC bandwidth needed for heterodyne detection is twice that needed for homodyne detection. It is well known that in heterodyne detection there exists a frequency offset, i.e., the frequency difference between the local oscillator (LO) source and a received optical signal. Thus, in the case where the ADC bandwidth is limited and the signal spectrum is wide (e.g., larger than the ADC bandwidth), the prior art does not optimize the frequency offset for heterodyne detection, resulting in undesirable signal spectrum overlap and/or cutoff.